The battle over the Market Basket grocery empire is headed for another big showdown Friday with employees planning a rally outside company headquarters in support of recently ousted president, Arthur T. Demoulas, while the new bosses are threatening to fire any workers who walk out on the job.

On Thursday, protesting workers had issued a 4:30 p.m. deadline for Market Basket executives to respond to their demands that Demoulas be reinstated. Instead, the newly appointed co-chief executives, Felicia Thornton and James F. Gooch, sent a note to the chain’s employees warning them not to skip work in support of Demoulas.

“If you choose to abandon your job or refuse to perform your job requirements, you will leave us no choice but to permanently replace you,” Thornton and Gooch wrote, according to a copy of the letter obtained by The Boston Globe.

The letter further incensed many of the workers, who peppered a Facebook page and Twitter accounts with calls of solidarity. A rallying message was also posted on a website set up by some of the protesting employees, wearemarketbasket.com, saying that the 120 or so managers and office workers at company headquarters in Tewksbury “will not be going to work” Friday.

“They will be backing up their words with actions and will be standing up for something they care so much for,” the workers wrote.

It is unclear how many store employees will attend the rally Friday — and how many will skip work to do so. The company has 71 stores in Massachusetts, New Hampshire, and Maine, and it employs about 25,000 people.

Already some stores are bracing for a sparse turnout of scheduled workers. Store managers in Burlington, for example, said they expect to have only a skeleton staff on hand, and weren’t even sure they would be getting their usual deliveries from company warehouses.

Even so, the Burlington store managers were united with the rank and file in supporting Demoulas and defying the company’s bosses.

“We consider ourselves stronger than a union,” said John Garon, a Burlington store manager who said he planned to attend Friday’s rally in Tewksbury. “There isn’t a single customer out there saying, ‘Shut up and do your job.’ They’re saying, ‘Give ’em hell.’ ”

The back and forth Thursday was the latest extraordinary turn in a decades-long feud between two branches of the Demoulas family for control of Demoulas Super Markets Inc., the multibillion dollar parent company of Market Basket. Arthur T. Demoulas was at the helm until late June, when he was fired by a board controlled by his cousin and chief rival Arthur S. Demoulas.

The board said that Arthur T. had been insubordinate and spent money recklessly. The feud dates to the 1970s, when the family of Arthur S. accused the Arthur T. side of cheating them out of company shares. Since then the cousins have fought inside the boardroom and the courtroom — and once with their fists during a break in a legal proceeding.

But Arthur T. Demoulas was popular among Market Basket employees, and this week they began an unusual public campaign to get their old boss his old job back. They have papered the company headquarters and some stores with signs and pamphlets in support, boasting messages such as, “We got your back Mr. D.”

Then organizers of the campaign issued a “nonnegotiable” ultimatum to Thornton and Gooch in a letter demanding Arthur T. Demoulas be reinstated “with full authority,” and insisting “We will not work for anyone but ATD.”

Thornton, a former finance chief for Albertsons supermarkets, and Gooch, previously a president of RadioShack Corp., said in their Thursday response that Demoulas’s board of directors had called a special meeting Monday to discuss the demands from employees.

In a previous statement, the pair said they did not have the authority to reinstate Demoulas themselves. The new bosses did say that when they tried to talk to the protesting employees Wednesday about their Demoulas demands, they were rebuffed.

“These employees instead left the meeting,” Gooch and Thornton said, and did not provide them with a copy of the demand letter posted on Facebook and Twitter. “This behavior is not appropriate nor is it in keeping with Market Basket’s culture of respect.”

A year ago, when Arthur T. Demoulas’s position was under threat from his cousin, Market Basket employees staged a rally on his behalf that drew about 2,000 workers and supporters, according to Steve Paulenka, a 40-year Market Basket veteran who is among the leaders of the protest group.

Paulenka said employees were being encouraged but not required to attend, and Market Basket stores would remain open. “Take care of customers, that’s what the boss [Arthur T.] would want,” Paulenka said. But, “I made it clear if anyone wants to come, they should be allowed to punch out and come down.” About the rally, Paulenka added: “I’m either going to have a lot of people next to me, or I’m going to be looking for employment.”

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